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1. Merging Inductive Relations

   https://doi.org/10.1145/3591292  

   Prinz, Jacob; Lampropoulos, Leonidas (June 2023, Proceedings of the ACM on Programming Languages)

   Inductive relations offer a powerful and expressive way of writing program specifications while facilitating compositional reasoning. Their widespread use by proof assistant users has made them a particularly attractive target for proof engineering tools such as QuickChick, a property-based testing tool for Coq which can automatically derive generators for values satisfying an inductive relation. However, while such generators are generally efficient, there is an infrequent yet seemingly inevitable situation where their performance greatly degrades: when multiple inductive relations constrain the same piece of data. In this paper, we introduce an algorithm for merging two such inductively defined properties that share an index. The algorithm finds shared structure between the two relations, and creates a single merged relation that is provably equivalent to the conjunction of the two. We demonstrate, through a series of case studies, that the merged relations can improve the performance of automatic generation by orders of magnitude, as well as simplify mechanized proofs by getting rid of the need for nested induction and tedious low-level book-keeping. 

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2. Trust in Social Relations

   https://doi.org/10.1146/annurev-soc-082120-082850  

   Schilke, Oliver; Reimann, Martin; Cook, Karen S. (July 2021, Annual Review of Sociology)

   null (Ed.)

   Trust is key to understanding the dynamics of social relations, to the extent that it is often viewed as the glue that holds society together. We review the mounting sociological literature to help answer what trust is and where it comes from. To this end, we identify two research streams—on particularized trust and generalized trust, respectively—and propose an integrative framework that bridges these lines of research while also enhancing conceptual precision. This framework provides the springboard for identifying several important avenues for future research, including new investigations into the radius of trust, the intermediate form of categorical trust, and the interrelationships between different forms of trust. This article also calls for more scholarship focusing on the consequences (versus antecedents) of trust, addressing more fully the trustee side of the relation, and employing new empirical methods. Such novel approaches will ensure that trust research will continue to provide important insights into the functioning of modern society in the years to come. Expected final online publication date for the Annual Review of Sociology, Volume 47 is July 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates. 

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3. Equivalence relations and determinacy

   https://doi.org/10.1142/S0219061322500039  

   Crone, Logan; Fishman, Lior; Jackson, Stephen (April 2022, Journal of Mathematical Logic)

   We introduce the notion of [Formula: see text]-determinacy for [Formula: see text] a pointclass and [Formula: see text] an equivalence relation on a Polish space [Formula: see text]. A case of particular interest is the case when [Formula: see text] is the (left) shift-action of [Formula: see text] on [Formula: see text] where [Formula: see text] or [Formula: see text]. We show that for all shift actions by countable groups [Formula: see text], and any “reasonable” pointclass [Formula: see text], that [Formula: see text]-determinacy implies [Formula: see text]-determinacy. We also prove a corresponding result when [Formula: see text] is a subshift of finite type of the shift map on [Formula: see text]. 

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4. The Perception of Relations

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   Hafri, Alon; Firestone, Chaz (June 2021, Trends in Cognitive Sciences)

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5. Relations in bounded cohomology

   https://doi.org/10.1112/topo.12150  

   Farre, James (May 2020, Journal of Topology)